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a) Let n = (abc)7. Prove that n ≡ a + b + c (mod 6).
b) Use congruences to show that 4|32n - 1 for all integers n ≥ 0.
Definite Integral : Given a function f ( x ) which is continuous on the interval [a,b] we divide the interval in n subintervals of equivalent width, Δx , and from each interval se
Nora works at a laboratory as a chemist . she was told to prepare 100L of 25% alcohol solution. she has on hand of a 15% percent alcohol solution and a 40% alcohol solution which s
who discovered unitary method
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Cardioids and Limacons These can be split up into the following three cases. 1. Cardioids: r = a + a cos θ and r = a + a sin θ. These encompass a graph that is vaguel
Lucas purchased his motorcycle for $5,875.98 and sold it for $7,777.77. What was his profit? To ?nd out the pro?t, you must subtract what Lucas paid for the motorcycle from the
Linear Approximations In this section we will look at an application not of derivatives but of the tangent line to a function. Certainly, to get the tangent line we do have to
Calculate the edges in an undirected graph along with two vertices of degree 7, four vertices of degree 5, and the remaining four vertices of degree are 6? Ans: Total degree of
Probability Distributions Since the value of a random variable cannot be predicted accurately, by convention, probabilities are assigned to all the likely values that the varia
The Shape of a Graph, Part II : In previous we saw how we could use the first derivative of a function to obtain some information regarding the graph of a function. In this secti
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